The use of He's variational iteration method for solving a Fokker-Planck equation

Physica Scripta

Volumn 74, Issue 3, 2006, Pages 310-316

  Dehghan, Mehdi ^a   Tatari, Mehdi ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

ADOMIAN DECOMPOSITION METHOD; FOKKER-PLANCK EQUATION; PARABOLIC TYPE; VARIATIONAL ITERATION METHOD;

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; LAGRANGE MULTIPLIERS; NONLINEAR EQUATIONS; OPTIMIZATION; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

ITERATIVE METHODS;

EID: 33749530855     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/74/3/003     Document Type: Article

References (34)

1. Ganji D D The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer Phys. Lett. A 355 337-41
2. He J H 2002 Approximate Analytical Methods in Science and Engineering (Zhengzhou: Henan Sci. and Tech. Press) (in Chinese)
3. He J H 1997 Variational iteration method for delay differential equations Commun. Nonlinear Sci. Numer. Simulat. 2 235-6
4. He J H 1998 Approximate solution of nonlinear differential equations with convolution product non-linearities Comput. Methods. Appl. Mech. Eng. 167 69-73
5. He J H 1998 Approximate analytical solution for seepage flow with fractional derivatives in porous media Comput. Methods Appl. Mech. Eng. 167 57-68
6. He J H 1999 Variational iteration method a kind of non-linear analytical technique: some examples Int. J. Nonlinear Mech. 34 699-708
7. He J H 2000 Variational iteration method for autonomous ordinary differential systems Appl. Math. Comput. 114 115-23
8. He J H, Wan Y Q and Guo Q 2004 An iteration formulation for normalized diode characteristics Int. J. Circuit Theory Appl. 32 629-32
9. Inokuti M, Sekine H and Mura T 1978 General use of the Lagrange multiplier in non-linear mathematical physics Variational Methods in the Mechanics of Solids (New York: Pergamon) pp 156-62
10. Momani S and Abuasad S 2006 Application of He's variational iteration method to Helmholtz equation Chaos Solitons Fractals 27 1119-23
11. Abdou M A and Soliman A A 2005 Variational iteration method for solving Burger's and coupled Burger's equations J. Comput. Appl. Math. 181 245-51
12. Draganescu Gh E and Capalnasan V 2003 Nonlinear relaxation phenomena in polycrystalline solids Int. J. Nonlinear Sci. Numer. Simul. 4 219-25
13. Momani S and Odibat Z Analytical approach to linear fractional partial differential equations arising in fluid mechanics Phys. Lett. A 355 271-9
14. Momani S and Odibat Z Numerical comparison of methods for solving linear differential equations of fractional order Chaos Solitons Fractals at press
15. Odibat Z and Momani S 2006 Application of variational iteration method to nonlinear differential equations of fractional order Int. J. Nonlinear Sci. Numer. Simul. 7 27-34
16. Sweilam N H and Khader M M Variational iteration method for one dimensional nonlinear thermoelasticity Chaos Solitons Fractals at press
17. Abdou M A and Soliman A A 2005 New applications of variational iteration method Physica D 211 1-8
18. Dehghan M 2004 The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure Int. J. Comput. Math. 81 979-89
19. Draganescu Gh E, Cofanb N and Rujanc D L 2005 Nonlinear vibrations of a nano sized sensor with fractional damping J. Optoelectron. Adv. Mater. 7 877-84
20. He J H and Wu X H 2006 Construction of solitary solution and compacton-like solution by variational iteration method Chaos Solitons Fractals 29 108-13
21. Jumarie G 2004 Fractional Brownian motions via random walk in the complex plane and via fractional derivative, comparison and further results on their Fokker-Planck equations Chaos Solitons Fractals 22 907-25
22. Kamitani Y and Matsuba I 2004 Self-similar characteristics of neural networks based on Fokker-Planck equation Chaos Solitons Fractals 20 329-35
23. Xu Y, Ren F Y, Liang J R and Qiu W Y 2004 Stretched Gaussian asymptotic behavior for fractional Fokker-Planck equation on fractal structure in external force fields Chaos Solitons Fractals 20 581-6
24. Zak M 2006 Expectation-based intelligent control Chaos Solitons Fractals 28 616-26
25. Risken H 1989 The Fokker-Planck Equation: Method of Solution and Applications (Berlin: Springer)
26. Frank T D 2004 Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations Physica A 331 391-408
27. Buet C, Dellacherie S and Sentis R 2001 Numerical solution of an ionic Fokker-Planck equation with electronic temperature SIAM J. Numer. Anal. 39 1219-53
28. Harrison G 1988 Numerical solution of the Fokker-Planck equation using moving finite elements Numer. Methods Partial Differ. Eqns 4 219-32
29. Palleschi V and de Rosa M 1992 Numerical solution of the Fokker-Planck equation. II. Multidimensional case Phys. Lett. A 163 381-91
30. Palleschi V, Sarri F, Marcozzi G and Torquati M R 1990 Numerical solution of the Fokker-Planck equation: a fast and accurate algorithm Phys. Lett. A 146 378-86
31. Vanaja V 1992 Numerical solution of simple Fokker-Planck equation Appl. Numer. Math. 9 533-40
32. Zorzano M P, Mais H and Vazquez L 1999 Numerical solution of two-dimensional Fokker-Planck equations Appl. Math. Comput. 98 109-17
33. He J H 2003 Generalized Variational Principles in Fluids (Hong Kong: Science and Culture Publishing House of China) (in Chinese)
34. Dehghan M 2006 Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices Math. Comput. Simul. 71 16-30